Final answer:
Corollaries and Theorems require proof in a logical system, while Postulates and Axioms are accepted without proof as foundational truths. Theorems require a combination of proofs, whereas Corollaries may need further proof in some contexts. So the correct options are A and B.
Step-by-step explanation:
In a logical system, the statements that require proof are Corollaries and Theorems. A Corollary is a proposition that follows with little or no proof required from one already proven. However, it often gets further scrutiny and might need additional proof depending on the context. Theorems, on the other hand, are statements that require proof, typically involving a combination of known facts, axioms, and previously established theorems.
Postulates and Axioms do not require proof within a logical system because they are assumptions that are accepted as true without proof. They provide the foundational truths on which the logical system is built.
To give an example in the context of logical reasoning, consider a conditional statement: 'If it is raining, then the ground is wet.' Here, 'it is raining' is the sufficient condition, and 'the ground is wet' is the necessary condition. To prove a conditional statement false, one must provide a counterexample where the premise is true, but the conclusion is false.